Question

f(x)= (x^2-1)^3,is its derivative f'(x)= 6x^5 -12x^3 + 6x.

Is there an alternative answer, because a computer generated answer is diff then mine. please help.

Answer 1

yes, that's the derivative.
did you expand your answer? or how did you do it?

Answer 2

I used the chain rule... my working is above
y = u^3 where u= (x^2-1)

so dy/du = 3u^2
and du/dx = 2x

then dy/dx = 3u^2(2x)
so after that substitute u

3(x^2-1)^2(2x)
=6x(x^2-1)^2
and I expanded it and got
6x^5-12x^3+6x

is that correct?
because a computer generated answer says you can simplify (x^2-1) since it is a perfect square and they get a diff answer than mine? However i cannot understand their simplification.

Answer 3

yes, your answer is correct. :)

i think that simplification means to factor 6x(x^2-1)^2 into 6x[(x-1)^2][(x+1)^2]

Answer 4

I majorly confused here, I am using a computer software which gives me a different answer and i am doubting my work over an over again, the computer software tells me:
"squaring the expression means multiplying the expression by itself"

and then they expand 6x[(x-1)(x-1)][x+1]^2
and in the next step then suddenly (x-1) is canceled and they just consider (x+1)(x+1)

Can someone explain me why the software does that, or is it just one of their ways to trick its users?